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A Remain campaigner, he is meeting key figures including EU chief negotiator Michel Barnier and the European Parliament’s Brexit Co-ordinator Guy Verhofstadt.

Mr Graham said: “The next few weeks are critical. If the EU decides, for whatever reasons, that not enough progress has been made on citizens' rights, and cannot agree on People issues, nor move to the next phase of talks (ie the transition) then there is a real risk of the NO deal camp more successfully arguing their case.

“So this is a key moment and we must do all we can to resolve citizens' rights and the Irish situation.

“Meeting key players here - those leading the Brexit negotiations on the European side as well as British officials based in Brussels and Paris working on Brexit - helps clarify both the risks and opportunities.

“My concern is that the EU underestimates the risk of squeezing us so much in the negotiations that a deal becomes very hard to achieve. So the December talks are critical."

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He will visit both Brussels and Paris this week with others from the UK Government’s Brexit Select Committee to meet the political heavyweights along with the UK’s ambassadors to the EU and France and many others including government, parliamentarians and the head of the French CBI.

His comments come as both sides try to agree reach an agreement over two main issues – the cost of the UK’s divorce bill (how much the UK will pay back to the EU for leaving); and the future of EU citizens in the UK and likewise UK citizens in the EU.

After several months of negotiations, along with intervention by the UK Prime Minister Theresa May, the deadlock continues to hold.